What is the range of "x-y is a rational number"? Where x and y are set of real numbers.

is it -- (0,0), (1/2,-1/2), (1/3, 4/3)?

Your question is confusing. A function maps the members of the set A to members of the set B. The set A is called the domain and B is called the range. (To put it in simple terms anyway.) To define an expression "x - y" is a rational number where x and y are the set of real numbers makes little sense to me.

Now, if you are merely asking what is the size of the set (i.e. The set of all real numbers x and y such that x - y is rational) then your answer is that the size of your set is infinite. Given any value of x we can find an infinite number of y values such that x - y is rational.

Your question is confusing. A function maps the members of the set A to members of the set B. The set A is called the domain and B is called the range. (To put it in simple terms anyway.) To define an expression "x - y" is a rational number where x and y are the set of real numbers makes little sense to me.

Now, if you are merely asking what is the size of the set \{ x - y \in \mathbb{Q}|x, y \in \mathbb{R} \} (i.e. The set of all real numbers x and y such that x - y is rational) then your answer is that the size of your set is infinite. Given any value of x we can find an infinite number of y values such that x - y is rational.

I think this addresses your question. If not, just let me know.

-Dan

My mistake its not "Range" it is the topic of "Relations" - I just have to find the pair of elements given the "condition of the relation" i.e. x-y is a rational no., So I am wondering what the pair of elements might be...